Student T Distribution
Student T Distribution
The Student t distribution with n degrees of freedom is the continuous probability distribution with the following probability density function:
The notation X ~ Tn denotes that the random variable X has a Student t distribution with n degrees of freedom. The random variable X is also the quotient of two independent random variables, the dividend being a standard normal variable and the divisor the square root of a random variable with a chi-square distribution with n degrees of freedom divided by n. That is, if Z and Y are independent,
The Student t distribution with n degrees of freedom has a graph that is symmetric about the y-axis and is very similar to that of the standard normal distribution. However, its graph flatter than that of the standard normal distribution, with more area in its tails. But as n increases, the Student t distribution converges to the standard normal distribution.
The Upper Percentiles of the Student's t-Distribution Tables of any Statistics book tabulates the values of upper percentiles for the Student t distribution with n degrees of freedom, for selected values of n from 1 to 120. Since the Student t distribution has a symmetric distribution about x = 0, the values of its lower percentiles can be derived from the values of its upper percentiles. For X ~ Tn,
 